Automatic Extraction of Ordinary Differential Equations from Data: Sparse Regression Tools for System Identification

Studying nonlinear systems across engineering, physics, economics, biology, and chemistry often hinges upon successfully discovering their underlying dynamics. However, despite the abundance of data in today's world, a complete comprehension of these governing equations often remains elusive, posing a significant challenge. Traditional system identification methods for building mathematical models to describe these dynamics can be time-consuming, error-prone, and limited by data availability. This thesis presents three comprehensive strategies to address these challenges and automate model discovery. The procedures outlined here employ classic statistical and machine learning methods, such as signal filtering, sparse regression, bootstrap sampling, Bayesian inference, and unsupervised learning algorithms, to capture complex and nonlinear relationships in data. Building on these foundational techniques, the proposed processes offer a reliable and efficient approach to identifying models of ordinary differential equations from data, differing from and complementing existing frameworks. The results presented here provide rigorous benchmarking against state-of-the-art algorithms, demonstrating the proposed methods' effectiveness in model discovery and highlighting the potential for discovering governing equations across applications such as weather forecasting, chemical reaction and electrical circuit modelling, and predator-prey dynamics. These methods can aid in solving critical decision-making problems, including optimising resource allocation, predicting system failures, and facilitating adaptive control in various domains. Ultimately, the strategies developed in this thesis are designed to integrate seamlessly into current workflows, thereby promoting data-driven decision-making and enhancing understanding of complex system dynamics.